EQUILIBRIUM SIZE DISTRIBUTIONS OF CIRCULAR DOMAINS IN AMPHIPHILIC MONOLAYERS

An expression is derived for the free energy of a surfactant monolayer at the interface between two immiscible bulk phases for a range of su rface pressures in which two surface phases coexist. The condensed pha se is assumed to be present in dispersed form, viz., as circular domai ns embedded in the less dense phase. The domains are kept in fixed pos itions as a result of electrostatic trapping. A thermodynamic analysis is presented on the basis of the free energy expression for the case of a single amphiphilic component using a mass-action equilibrium cond ition, which yields the equilibrium distribution of domain sizes. The distribution function is shown to be the result of a competition betwe en a collective entropy effect (which favors dispersion), line tension , electrostatic edge effects, and interdomain repulsion, while a possi ble contribution due to bending elasticity of the phase boundary is ta ken into account. A numerical example illustrates that for practical s ystems the distributions are fairly narrow and that both the domain si ze and the width of the distribution increases with the fractional sur face coverage of the condensed phase, but in such a way that the degre e of polydispersity decreases.